EXISTENCE OF NONOSCILLATORY SOLUTIONS OF HIGHER-ORDER NONLINEAR NEUTRAL DELAY DIFFERENCE EQUATIONS

This paper studies the existence of nonoscillatory solutions of a higher-order nonlinear neutral delay difference equation Delta (a(kn) . . . Delta(a(2n) Delta(a(1n) Delta(x(n) + b(n) x(n-d))))) + f, ( n, x(n-r1n), x(n-r2n) ,..., x(n-rsn) ) = 0, n >= n(0) , where n(0) >= 0, n >= 0, d > 0, k > 0, s > 0 are integers, {a(in)} n >= n(0) (i = 1, 2,..., k) and {b(n)}(n > n0) are real sequences, f : {n : n >= n(0)} x R-s -> R is a mapping and boolean OR (s)(j) = 1 {r(jn)} (n >= n0) subset of Z. By applying Krasnoselskii's Fixed Point Theorem, some sufficient conditions for the existence of nonoscillatory solutions of this equation are established and indicated through five theorems according to the range of value of the sequence b(n) .